﻿ 水声目标辐射噪声谐波特征提取算法
 舰船科学技术  2017, Vol. 39 Issue (9): 133-137 PDF

1. 海军航空工程学院 电子信息工程系，山东 烟台 264001;
2. 中国人民解放军92635部队，山东 青岛 266000

Harmonic feature extraction algorithm for radiated noise of underwater acoustic target
LIANG Wei1,2, LIU Fu-xiao2, YANG Ri-jie1
1. Department of Electronic Information Engineering, Naval Aeronautics and Astronautics University, Yantai 264001, China;
2. No. 92635 Unit of PLA, Qingdao 266000, China
Abstract: The harmonic components for radiated noise of underwater-target contain information reflecting nature of target itself, and extracting effectively target harmonic is related to result of target recognition. By combining likelihood estimation method and Kalman filtering tracking approach, a new feature extraction algorithm was developed to extract the harmonic feature from the underwater noise radiated. The likelihood estimation method gives an estimation of the instant fundamental frequency, while Kalman filter is adopted to capture the time varying structure. The fundamental frequency tracks are then used to extract the amplitudes of harmonics and obtain harmonic feature of target. Based on the comparison of simulated signal and the measured data, feasibility is verified of harmonic feature extraction algorithm estimating undamental frequency and extracting harmonic information.
Key words: underwater acoustic target     radiated noise     harmonic     feature extraction
0 引　言

1 水声目标辐射噪声信号模型

 $\begin{split}r(t) = & s(t) + n(t)=\\& \sum\limits_{h = 1}^H {{A_h}} \cos (2\pi h\gamma t + {\varphi _h}) + n(t)\end{split}\text{。}$ (1)

 $\begin{split}r(t,\theta ) = & s(t,\theta ) + n(t)=\\& \sum\limits_{h = 1}^H {{A_h}} \cos (2\pi h\gamma (t)t + {\varphi _h}) + n(t)\end{split}\text{。}$ (2)

 $S(f,{\theta _k}) = \sum\limits_{h = 1}^H {\frac{{{A_h}}}{2}} \sin {\mathop c\nolimits} [\pi (f - h{\gamma _k})]\text{，}$ (3)

 ${R_{ko}}(m\Delta f,{\theta _k}) \!=\! \frac{2}{{{N_S}}}\sum\limits_{n = - {N_S}/2}^{{N_S}/2 - 1} {{r_k}} ({t_k} \!\!+\! n\Delta t,{\theta _k}){e^{ - jm2\pi \Delta fn\Delta t}}\text{。}\!\!$ (4)

2 水声目标辐射噪声谐波特征提取方法

2.1 基频估计方法

 $\begin{split}{C_{mp}} =& S({f_m},{\theta _k}|{\gamma _k} = {\zeta _p},{A_h} = 2)=\\& \sum\limits_{h = 1}^H {\sin {\mathop c\nolimits} \left[ {\pi ({f_m} - h{\zeta _p})} \right]}\text{。}\end{split}$ (5)

 $\rho \left( t \right) = \frac{{E\left[ {\left( {X\left( t \right) - {\mu _x}\left( t \right)} \right)\left( {Y\left( t \right) - {\mu _y}\left( t \right)} \right)} \right]}}{{\sqrt {E\left[ {{{\left( {X\left( t \right) - {\mu _x}\left( t \right)} \right)}^2}} \right]E\left[ {{{\left( {Y\left( t \right) - {\mu _y}\left( t \right)} \right)}^2}} \right]} }}\text{，}$ (6)

ρt）取值在[–1，1]间。要估计tk时刻接收信号 ${R_k}({f_m},{\theta _k})$ 的基频，则需计算样本信号模型与接收信号间的互相关函数[4]

 ${\hat \rho _{pk}}({\zeta _p},{t_k}) = \frac{{\sum\nolimits_{fm} {({C_{mp}} - {\mu _C}){R_k}({f_m},{\theta _k})} }}{{\sqrt {\sum\nolimits_{fm} {{{({C_{mp}} - {\mu _C})}^2}} } \sqrt {\sum\nolimits_{fm} {{R_k}{{({f_m},{\theta _k})}^2}} } }}\text{。}$ (7)

2.2 基频最优估计 2.2.1 基于卡尔曼滤波理论的基频跟踪

 ${\hat{ \varGamma }}_k^ - = {{F}}{{\hat{ \varGamma }}_{k - 1}} \text{，}\;\;\;{{P}}_k^ - = {{F}}{{{P}}_{k - 1}}{{F}^{\rm T}} + {{Q}} \text{。}$ (8)

 \left\{ \begin{aligned}& {K_k} = {{P}}_k^ - {{{H}}^{\rm T}}{({{HP}}_k^ - {{{H}}^{\rm T}} + {{R}})^{ - 1}}\\& {{{\hat{ \varGamma }}}_k} = {\hat{ \varGamma }}_k^ - + {K_k}({{\bf{z}}_k} - {{{\rm H}\hat \Gamma }}_k^ - )\\& {{{P}}_k} = ({{I}} - {K_k}{{H}}){{P}}_k^ - \end{aligned} \right. (9)

2.2.2 基频跟踪算法

 $\left\{ {\begin{array}{*{20}{l}}{{{{\varGamma }}_k} = {{F}}{{\bf{\varGamma }}_{k - 1}} + {{{w}}_k}}\text{，}\\{{{{\varGamma }}_k} = {{[{\gamma _{KF,k}},{{\dot \gamma }_{KF,k}},{\rho _{KF,pk}}]}^{\rm T}}}\text{，}\\{{{F}} = \left[ {\begin{array}{*{20}{c}}1 & 1 & 0\\0 & 1 & 0\\0 & 0 & 1\end{array}} \right]}\text{，}\\{{{{w}}_k} \sim N({{0}},{{Q}})}\text{。}\end{array}} \right.$ (10)

 $\left\{ {\begin{array}{*{20}{l}}{{{{z}}_k} = {{H}}{{{\varGamma }}_k} + {v_k}}\text{，}\\{{{{z}}_k} = {{[{{\hat \gamma }_k},{{\hat \rho }_{pk}}]}^{\rm T}}}\text{，}\\{{{H}} = \left[ {\begin{array}{*{20}{c}}1 & 0 & 0\\0 & 0 & 1\end{array}} \right]}\text{，}\\{{v_k} \sim N(0,R)}\text{。}\end{array}} \right.$ (11)

 ${{Q}} = \left[ {\begin{array}{*{20}{c}}{{Q_\gamma }} & 0 & 0\\0 & {{Q_{\dot \gamma }}} & 0\\0 & 0 & {{Q_\rho }}\end{array}} \right]\text{，}\;\;\;{{R}} = \left[ {\begin{array}{*{20}{c}}{{R_\gamma }} & 0\\0 & {{R_\rho }}\end{array}} \right]\text{。}$ (12)

2.2.3 基频跟踪逻辑

 $({z_k} - H\hat \Gamma _k^ - ){(HP_k^ - {H^{\rm T}} + R)^{ - 1}}{({z_k} - H\hat \Gamma _k^ - )^{\rm T}} < {\chi ^2}\text{。}$ (13)

2.3 谐波特征提取

 ${\bf{\psi }}\left[ k \right] = \sqrt {\frac{1}{L}\sum\limits_{k = 1}^L {{{\left| {{\rho _{KF,pk}}\left[ k \right]} \right|}^2}} } \text{。}$ (14)

3 仿真结果与分析

 图 1 基频跟踪在谱图上的投影 Fig. 1 Projection of fundamental frequency tracking on the spectrogram

 图 2 各阶谐波与背景噪声的相对振幅特性 Fig. 2 The relative amplitude characteristics of harmonics and background noise

4 结　语

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